Quick guide
How to use this calculator
- Enter non-negative values.
- Choose power p from −100 to 100.
- Compare named cases p=−1, 0, 1, and 2 without changing the dataset.
Calculation method
Raise, average, then undo the power
For p≠0, the power mean is the pth root of the mean of xᵖ. At p=0 its continuous limit is the geometric mean. Log-space evaluation avoids unsafe intermediate powers.
Worked example
Recover RMS as a power mean
For 3 and 4, choosing p=2 gives the quadratic mean.
M₂ = √[(3²+4²)/2] = √12.5
Supported inputs
Precision and limits
List size
Add 1–100 labelled value rows.
Decimal size
Each value may contain up to 200 digits and 100 decimal places.
Exactness
Exact rational results are never replaced by a rounded decimal; approximations are labelled.
Domain
Negative values are excluded. A zero with negative p follows the standard generalized-mean zero convention.
Numerical result
Generalized results are approximations; p is limited to avoid a visually different but numerically indistinguishable extremum calculation.